Abstract: In this talk, I will explain some interesting intersection
formula between Hirzebruch-Zagier divisors and CM cycles on a Hilbert
modular surface over Z, and its applications. Among the
applications are a non-abelian generalization of the well-known
Chowla-Selberg formula as reformulated by Colmez, and a conjecture of
Lauter on CM values of Igusa invariants.